A young man is pushing a baby carriage at a constant...

A young man is pushing a baby carriage at a constant velocity along a level street. A friend comes by to chat and the young man lets go of the carriage. It rolls on for a bit, slows, and comes to a stop. At time $t=0$ the young man is walking with a constant velocity. At time $t_{1}$ he releases the carriage. At time $t_{2}$ the carriage comes to rest. Sketch qualitatively accurate (i.e., we don't care about the values but we do care about the shape) graphs of each of the following variables versus time: (a) position of the carriage, (b) velocity of the carriage, (c) acceleration of the carriage, (d) net force on the carriage, (e) force the man exerts on the carriage, (f) force of friction on the carriage. Be sure to note the important times $t=0, t_{1}$, and $t_{2}$ on the time axes of your graphs. Take the positive direction to be the direction in which the man was initially walking.

A young man is pushing a baby carriage at a constant velocity along a level street. A friend comes by to chat and the young man lets go of the carriage. It rolls on for a bit, slows, and comes to a stop. At time $t=0$ the young man is walking with a constant velocity. At time $t_{1}$ he releases the carriage. At time $t_{2}$ the carriage comes to rest. Sketch qualitatively accurate (i.e., we don't care about the values but we do care about the shape) graphs of each of the following variables versus time:
(a) position of the carriage, (b) velocity of the carriage, (c) acceleration of the carriage, (d) net force on the carriage, (e) force the man exerts on the carriage, (f) force of friction on the carriage. Be sure to note the important times $t=0, t_{1}$, and $t_{2}$ on the time axes of your graphs. Take the positive direction to be the direction in which the man was initially walking.

Key Concepts

Kinematics of Motion

This concept covers the relationships between position, velocity, and acceleration over time. In problems like this, recognizing that a constant velocity corresponds to a linear position graph (with a constant slope) while a uniform deceleration produces a curved position graph (whose slope decreases steadily) is essential. Understanding these relationships allows one to sketch qualitative curves that reflect periods of constant motion, deceleration, and rest.

Newton's Second Law

Newton’s Second Law (F_net = m·a) is the fundamental principle connecting net force, mass, and acceleration. In the context of this problem, it explains that while the carriage is being pushed at constant velocity before its release (zero net force and zero acceleration), the moment the man lets go the only unbalanced force is friction, which imparts a negative acceleration until the carriage stops.

Friction

Friction is the force that resists the relative motion of two surfaces in contact. For the baby carriage, friction acts in the direction opposite to its motion. After the man releases the carriage, friction is the net force that gradually decelerates the carriage. Its constant (or nearly constant) magnitude leads to a constant negative acceleration phase in the motion graphs.

Force Analysis

Force analysis involves breaking down and understanding the various forces acting on an object at different times. In this problem, before the release (t < t1), the man’s applied force exactly balances friction, resulting in zero net force and constant velocity. After the carriage is released, the man’s force drops to zero and friction becomes the net force causing deceleration. This analysis is critical in sketching the graphs for net force and the man’s force over time.

Graphical Interpretation of Physical Quantities

This concept emphasizes the translation of physical principles into qualitative graphs. It involves recognizing key times—such as the release time (t1) and the stopping time (t2)—and understanding how the motion and forces change at these intervals. The transition from constant motion to deceleration and finally to rest must be reflected in the graphs for position (changes in slope), velocity (a drop from a constant value to zero), acceleration (a step change from zero to a constant negative value and back to zero), and in the depiction of the forces involved.

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